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If f(x)=∫​ 2sinx-sin2x dx/x 3​ ​​ ,x is not equal to zero, then find lim f’ (x) as x tends to zero. ​

If f(x)=∫​ 2sinx-sin2x dx/x 3​ ​​ ,x is not equal to zero, then find lim f’ (x) as x tends to zero.

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
The differentiation of the integeral,
f(x)=∫​ 2sinx-sin2x dx/x 3​ ​​
would give
f(x) simply.
that is:
lim x  – > 0 (2sinx-sin2x) /x 3
Simply expand the exapnsion of sin terms up to the x^3 terms so that it would get cancel out from the denominator x term.
and then put x = 0 as the limit.​ ​​

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